n^2-2n+1=2

Simple and best practice solution for n^2-2n+1=2 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for n^2-2n+1=2 equation:


Simplifying
n2 + -2n + 1 = 2

Reorder the terms:
1 + -2n + n2 = 2

Solving
1 + -2n + n2 = 2

Solving for variable 'n'.

Reorder the terms:
1 + -2 + -2n + n2 = 2 + -2

Combine like terms: 1 + -2 = -1
-1 + -2n + n2 = 2 + -2

Combine like terms: 2 + -2 = 0
-1 + -2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + -2n + n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2n + n2 = 0 + 1
-2n + n2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2n + n2 = 1

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = 1 + 1

Reorder the terms:
1 + -2n + n2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + -2n + n2 = 2

Factor a perfect square on the left side:
(n + -1)(n + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(n + -1) equal to 1.414213562 and -1.414213562.

Subproblem 1

n + -1 = 1.414213562 Simplifying n + -1 = 1.414213562 Reorder the terms: -1 + n = 1.414213562 Solving -1 + n = 1.414213562 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + n = 1.414213562 + 1 n = 1.414213562 + 1 Combine like terms: 1.414213562 + 1 = 2.414213562 n = 2.414213562 Simplifying n = 2.414213562

Subproblem 2

n + -1 = -1.414213562 Simplifying n + -1 = -1.414213562 Reorder the terms: -1 + n = -1.414213562 Solving -1 + n = -1.414213562 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + n = -1.414213562 + 1 n = -1.414213562 + 1 Combine like terms: -1.414213562 + 1 = -0.414213562 n = -0.414213562 Simplifying n = -0.414213562

Solution

The solution to the problem is based on the solutions from the subproblems. n = {2.414213562, -0.414213562}

See similar equations:

| 12(2+12)=15 | | 30x^3y^2-5x^2y^3= | | 4*x^2-72*x+195=0 | | 7x-7y=-28 | | 2x+(y+z)=(2x+y)+z | | f(x)=0.75x^2-5 | | A=150(0.5)^2/5.7 | | 150(0.5)^2/5.7= | | lnx=ln(x+1)-1 | | X^3-x^2+25x-25=0 | | x(6x-7)=130 | | 16y^4-8y^3= | | (5b-9y)/(4b)-(b-6y)/(4b) | | 12k+3=9k | | (4x-70)+x=180 | | (6x-260)+x=90 | | x^2+18=243 | | (a^3b^4)/a^5b^-4 | | 15x+13=7x-19 | | n-7n=0 | | (8/7)/(16/7)=x | | (4x-85)+x=90 | | (9/16)/(7/9)=x | | (27/4)/(3/4)=x | | 16-8n-1=n-15n-3+7n | | 873/(291/4)=x | | -19=1+4m+6m | | 200/(154/9)=x | | 22/(11/7)=x | | 2n-n=-2 | | (29/6)/(7)=x | | (7/9)/(1/8)=x |

Equations solver categories